no, if you give mains then you are eligible for jossa counselling.

No , it is not necessary to qualify jee advanced.

Even a student who was not appeared in jee advanced is eligible to register in jossa . If u have just appeared in jee mains then you are eligible to sit  in jossa counsellimg.

Hope the question is answered

Yes.

If you are aiming for IITs then the eligibility criteria of JEE Advanced will be used for admission into IITs and JEE Main criteria will be used for NITs, IIITs and GFTIs. 

For reference, you can go through the below links -

https://engineering.careers360.com/articles/josaa-counselling

https://engineering.careers360.com/articles/josaa-eligibility-criteria

Good Luck!!!